To correctly translate this expression you would have to provide additional context about what "estado civil de las personas" refers to in the text that you are translating (a birth certificate). It may very well refer to the marital status of the parents of the newborn in question and, if this is indeed the case, "marital status" is the correct answer.

But since many translators do not realize that "estado civil" is a much broader term and often refers to other "civil statuses" of the person, I am offering the following information:

In Spain and other Spanish-speaking civil code countries the expression "estado civil" is a much broader concept than “marital status” and, depending on the context, may refer to "matrimonio," "filiación," "edad," "capacidad" (or) "incapacidad judicial declarada," "nacionalidad" or "vecindad civil." When correctly translated as “marital status,” "estado civil" refers to whether a person is single ("soltero/a"), married ("casado/a"), widowed ("viudo/a") or divorced ("divorciado/a"). In the context of "filiación" (“filiation,” i.e., the “parent-child relationship”) "estado civil" refers to one’s status as "padre"/"madre" or "hijo"/"hija." With respect to "edad" (“age”), one may be "menor de edad" (a “minor” or “infant,” now called simply “child” in England) or "mayor de edad" (of “legal/full age,” i.e., one who has reached the “age of majority”). The "estado civil" of "capacidad" (“legal capacity”) includes the status of "capaz" (“competent”) or incapaz (“incompetent”) in the case of persons adjudicated incompetent by a court of law ("incapacitado judicialmente"). Under the "estado civil" of "nacionalidad," in Spain, for example, one may be "español" (a “Spanish national” or “citizen”), "extranjero" (a “foreign national” or “alien”) or "apátrida" (a “stateless person”). And the "estado civil" of "vecindad civil" refers to one’s region of habitual residence that determines his submission to general civil legislation (the "Código Civil") or to specific regional or local law ("derecho foral"). All of these "civil statuses" must be recorded on the "Registro Civil."

Sources: Luis Ribó, "Diccionario de Derecho", Editorial Bosch, Barcelona, 1995.

Mónica Ortiz Sánchez and Virginia Pérez Pino, "Diccionario jurídico para estudiantes", Editorial Tecnos, Madrid, 2002.